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A Brief Introduction to Crystal Structure

Explore the world of crystals, learn about crystal lattices, symmetry elements, and crystal structures. Understand how symmetry influences physical properties and classify crystals based on their symmetries.

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A Brief Introduction to Crystal Structure

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  1. A Brief Introduction to Crystal Structure Dr. Jerald V Ramaclus, Assistant professor, Department of Physics, St. Joseph´s College, Trichy-620002

  2. Outcomes • Know a crystal • Differentiate a crystalline and amorphous material • Know a crystal lattice • Understand various symmetry elements and operations • Relate symmetry and crystal structure • Classify crystals based on symmetries

  3. Valley JW et al. Hadean age for a post-magma-ocean zircon confirmed by atom-probe tomography. Nature Geoscience, 7, 219–223 (2014); doi: 10.1038/ngeo2075

  4. Crystal Cave, Mexico Gypsum crystals measuring up to 36 feet (11 meters) long and weighing up to 55 tons are considered largest natural crystals. Stefan Lovgren, (2007-04-06). "Giant crystal cave's mystery solved". National Geographic News

  5. Sewell, Chile Large Gypsum crystals Cubic Pyrite crystals

  6. Snow crystals

  7. LAB GROWN CRYSTALS Silicon crystals grown by Czochralski technique at BARC, India KDP crystals grown at NIF, Lawrence Livermore National Laboratory, USA

  8. CRYSTALS ARE DIFFERENT • Shape • Size • Colour • Transparency • Properties

  9. CLASSIFICATION OF MATERIALS Materials can be classified into two categories based on the arrangement of atoms or molecules. Crystalline Amorphous

  10. Lattice + Basis = Crystal structure + = The structure of crystals can be described by a lattice, with a group of atoms allocated to every lattice point Image credit: https://www.flickr.com/photos/wlodi/252462355

  11. UNIT CELL Image credit:Prof. Stephen Lower, Professor Emeritus (Chemistry) at Simon Fraser University

  12. 2D Bravais Lattices Auguste Bravais Image credit: Public Domain, https://commons.wikimedia.org/w/index.php?curid=472338

  13. Crystal Systems Image credit: Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.

  14. SYMMETRY • The consequences of periodicity of atoms results in the properties of symmetry. • The symmetry properties govern the physical properties of crystal. • When a physical system is subjected to some symmetry operations, the properties does not change.

  15. Symmetry in nature Photo by Arjun Haarith

  16. REFLECTION symmetry

  17. ROTATION symmetry In an axis of two-fold symmetry, the 001 bar face along the c-axis which are identical and marked in blue appears twice during one full rotation. Similarly there are crystals with 3, 4 and 6 fold symmetries.

  18. INVERSION symmetry A crystal has an inversion center if there is a point at which the cell remains invariant when the mathematical transformation r + -r is performed on it.

  19. translation symmetry

  20. POINT GROUP • The symmetry of the basis is called point-group symmetry • It involves rotations, inversion and reflection which leave the basis invariant • Produces 32 point group symmetries

  21. 3D Bravais Lattices Image credit: http://www.seas.upenn.edu/~chem101/sschem/solidstatechem.html

  22. SPACE GROUP • Combination of rotational symmetries of point groups and translational symmetries on a space lattice • Glide plane = reflection + translation • Screw axes = rotation + translation • 230 space groups

  23. Atomic resolution imaging of SrTiO3, using annular dark field (ADF) and annular bright field (ABF) detectors. Overlay- strontium (green), titanium (grey) and oxygen (red). Image credit: Magnunor, Scanning transmission electron microscopy srtio3 compare adf abf, CC BY-SA 4.0

  24. SUMMARY • A crystal is a periodic arrangement of atoms • Crystal structure = Lattice + Basis • A unit cell, is the basic building block of a crystal • The properties of the crystal arise from the symmetry of the crystal.

  25. SYMMETRY ELEMENTS 32 POINT GROUPS 7 CRYSTAL SYSTEMS Triclinic Monoclinic Orthorhombic Tetragonal Trigonal Hexagonal Cubic 14 BRAVAIS LATTICES Simple Simple,BaC Simple,BC, BaC, FC Simple, BC Simple Simple Simple, BC, FC Srew axes & Glide planes 230 SPACE GROUPS P1, Pī P2,P21,etc P222, P221, etc P4, P41, etc P3, P31, etc P6, P61, etc P23, F23, etc Ref: X-Ray Diffraction Crystallography-Introduction, Examples and Solved Problems, Yoshio WasedaEiichiro, Matsubara Kozo Shinoda, Springer

  26. For the Good and the True

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